1 MEASUREMENT OF STATIC AND DYNAMIC PERFORMANCE CHARACTERISTICS OF SMALL ELECTRIC PROPULSION SYSTEMS By Aron J. Brezina and Scott K. Thomas Department of Mechanical and Materials Engineering Wright State University Dayton, Ohio 45435 ABSTRACT Unmanned aerial vehicles are being utilized by numerous groups around the world for various missions. Most of the smaller vehicles that have been developed use commercially-off- the-shelf parts, and little information about the performance characteristics of the propulsion systems is available in the archival literature. In light of this, the aim of the present research was to determine the performance of various small-scale propellers in the 4.0 to 6.0 inch diameter range driven by an electric motor. An experimental test stand was designed and constructed in which the propeller/electric motor was mounted in a wind tunnel for both static and dynamic testing, and the results were compared to those from previous studies. For static testing, the coefficient of thrust, the coefficient of propeller power, and the total propulsive efficiency, defined as the ratio of the propeller output power to the electrical input power, were plotted versus the propeller rotational speed. For dynamic testing, the rotational speed of the propeller was held constant at regular intervals while the airspeed was increased from zero to the windmill state. The coefficient of thrust, the coefficient of propeller power and the propeller efficiency were plotted versus the advance ratio for various rotational speeds. The thrust and torque were found to increase with rotational speed, propeller pitch and diameter, and decrease with airspeed. Using the present results and data from archival and non-archival sources, it was found that the coefficient of thrust could not be correlated with propeller diameter for square propellers where D = P. For a family of propellers (same manufacturer and application), correlations for the coefficient of thrust, the coefficient of propeller power and the propeller efficiency could be improved by modifying either the coefficients or the advance ratio with D/P. This dimensionless ratio allows for the propeller pitch to be accounted for in the performance coefficients.
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1
MEASUREMENT OF STATIC AND DYNAMIC PERFORMANCE
CHARACTERISTICS OF SMALL ELECTRIC PROPULSION SYSTEMS
By
Aron J. Brezina and Scott K. Thomas
Department of Mechanical and Materials Engineering
Wright State University
Dayton, Ohio 45435
ABSTRACT
Unmanned aerial vehicles are being utilized by numerous groups around the world for
various missions. Most of the smaller vehicles that have been developed use commercially-off-
the-shelf parts, and little information about the performance characteristics of the propulsion
systems is available in the archival literature. In light of this, the aim of the present research was
to determine the performance of various small-scale propellers in the 4.0 to 6.0 inch diameter
range driven by an electric motor. An experimental test stand was designed and constructed in
which the propeller/electric motor was mounted in a wind tunnel for both static and dynamic
testing, and the results were compared to those from previous studies. For static testing, the
coefficient of thrust, the coefficient of propeller power, and the total propulsive efficiency,
defined as the ratio of the propeller output power to the electrical input power, were plotted
versus the propeller rotational speed. For dynamic testing, the rotational speed of the propeller
was held constant at regular intervals while the airspeed was increased from zero to the windmill
state. The coefficient of thrust, the coefficient of propeller power and the propeller efficiency
were plotted versus the advance ratio for various rotational speeds. The thrust and torque were
found to increase with rotational speed, propeller pitch and diameter, and decrease with airspeed.
Using the present results and data from archival and non-archival sources, it was found that the
coefficient of thrust could not be correlated with propeller diameter for square propellers where
D = P. For a family of propellers (same manufacturer and application), correlations for the
coefficient of thrust, the coefficient of propeller power and the propeller efficiency could be
improved by modifying either the coefficients or the advance ratio with D/P. This dimensionless
ratio allows for the propeller pitch to be accounted for in the performance coefficients.
2
NOMENCLATURE
propeller disk area, m2
wind tunnel test section area, m2
coefficient of propeller power coefficient of torque
coefficient of thrust
propeller diameter, m
fixture drag, N
figure of merit
height of the Pitot tube from the bottom of the wind tunnel test section, m
electrical motor current, Amperes
advance ratio
propeller rotational speed, rev/s
propeller pitch, m
atmospheric pressure, Pa
Pitot tube differential pressure, Pa
electrical input power, W
propeller output power, W
torque, N-m
particular gas constant, J/(kg-K)
goodness of fit parameter
measured thrust, N
corrected thrust, N
atmospheric temperature, K
electric motor voltage, Volts
free-stream velocity, m/s
corrected free-stream velocity, m/s
wind tunnel test section width and height, m Δ uncertainty
propeller efficiency
total propulsive efficiency
density, kg/m3
τ4 Glauert correction variable
INTRODUCTION
Interest in the performance of small propellers operating at low Reynolds numbers has
grown recently. The aerospace industry has developed numerous unmanned aerial vehicles
(UAVs) and has kept most of the data about the propulsion systems proprietary. Very little
information is available in the archival literature about the performance characteristics of these
motor and propeller combinations. The present research and others like it have aimed to gather
and compare information about these small propulsion systems so that proper motor and
3
propeller combinations can be selected for a given mission profile. Several papers were reviewed
that relate directly to the present work and provide direction for the research.
Brandt and Selig (2011) experimentally determined efficiency as well as coefficients of
thrust and power for low Reynolds number propellers. The parametric ranges were as follows:
Propeller diameter 9 ≤ D ≤ 11 inches, propeller rotational speed 1500 ≤ n ≤ 7500 RPM, and the
incoming air velocity ranged from zero (static) to the windmill state of each propeller, i.e.,
that point at which the propeller generates zero thrust. A test stand was built inside the UIUC
wind tunnel to measure thrust, torque, and propeller rotational speed. Freestream air velocity was
measured using a Pitot tube and one of two differential pressure transducers depending on the
airspeed range. Velocity corrections were applied to account for the change in upstream airspeed
at the Pitot tube created by the propeller as well as the pressure change created by the fairing and
the constriction of the propeller slipstream caused by the walls. In total, 79 propellers from four
different manufacturers were tested to find the coefficient of thrust, the coefficient of power and
the propeller efficiency, all of which were plotted against advance ratio. The designs of the
propellers ranged from those for electric motors to those used for fuel-powered engines. For each
test, the rotational speed of each propeller was fixed while the freestream airspeed was varied.
Four different values of propeller rotational speed (n = 3000, 4000, 5000, and 6000 RPM) were
tested for each of the propellers. The results show that the propeller efficiency increases with the
propeller speed. This is primarily due to the increase in Reynolds number as the propeller spins
faster. Overall, the propeller efficiency ranged from 28 ≤ ηP ≤ 65%. The propellers were also
tested statically, but the data is only available in the UIUC propeller database (Selig, 2012).
Gamble (2009) designed an intricate LabVIEW program to automatically collect data and
generate propeller performance plots. A dynamometer was constructed using beam-type load
cells to measure thrust and torque. The development of the LabVIEW program was detailed as
well as a procedure for carrying out the experiment. Propellers were tested for repeatability by
performing identical experiments over several days with two identical propellers. The results
primarily focus on the effect of the Reynolds number on thrust and power coefficients and
efficiency versus advance ratio. Thrust versus velocity was compared for propellers with
constant diameter and varying pitch. Lastly, advance ratio was modified by replacing diameter
with pitch in the equation for advance ratio. The optimal advance ratio is shown using this
technique. This allows for the optimal pitch of a model propeller to be selected to achieve
4
maximum efficiency. The diameter can then be chosen from plots of thrust versus velocity to
produce the required thrust for the airframe.
Deters and Selig (2008) performed static tests on smaller propellers ranging from 2.5 ≤ D
≤ 5 inches in diameter. Static coefficients of thrust and power as well as the figure of merit
(
√ , typically used to measure the efficiency of helicopters) using modified
coefficients of thrust and power that use disk area and tip speed were determined experimentally.
The test stand utilized a 0.3 kg load cell and a 25 oz-in torque transducer to measure thrust and
torque, respectively. Propeller rotational speeds ranging from 2500 ≤ n ≤ 27,000 RPM were
measured using an infrared detector. A schematic of the test stand indicated the locations of the
components and a fairing surrounding the load cell and torque transducer. Calibrations of the
components were performed and data was collected using a data acquisition board. The geometry
of each propeller was found using PropellerScanner software (Hepperle, 2003) to find the chord
and twist distribution. This was used to calculate the Reynolds number at the 75% chord
location. Results show that over the rotational speed range tested, the figure of merit remained
fairly constant throughout the test. The results also show that a larger diameter propeller is more
efficient than a smaller one, and a propeller with a lower pitch is more efficient than one with a
higher pitch.
Ol et al. (2008) took a more analytical approach to studying small propellers operating at
low Reynolds numbers. Iterative methods were used to calculate the coefficient of thrust, the
coefficient of torque, and the propeller efficiency using propeller momentum theory and blade-
element methods. Propellers were discretized by cutting and tracing sections as well as digital
scans. Leading and trailing edges were fitted to the UIUC propeller library so that the resulting
analysis in XFOIL would successfully converge. The iterative process for thrust was dependent
on the various Reynolds numbers across the propeller blade at a given rotational speed. Two
separate experimental setups were constructed to compare the numerical results. Propellers in the
6 ≤ D ≤ 12 inch range were tested in the Langley Research Center Basic Aerodynamics Research
Tunnel (BART) and larger propellers in the 14 ≤ D ≤ 20 inch range were tested in the AFRL
Vertical Wind Tunnel (VWT). Static tests were performed with the wind tunnel sides open to
alleviate the induced airflow velocity inside the wind tunnel. Blockage corrections were applied
to BART tests but not to VWT tests, since the tunnel diameter of the VWT was greater than five
times the diameter of the propellers tested. Drag on the test stand was corrected by sweeping
5
tunnel velocity and generating curve fits that were used to adjust the actual data. A large
sensitivity to twist distribution was observed in the tests and the analysis. Ol et al. postulated that
plots of torque coefficient versus advance ratio are sometimes misleading because they do not
account for Reynolds number effects. It was also shown that when the ratio of diameter to pitch
is scaled (10 × 10 to 12 × 12, for example) the experimental data fits together well within the
bounds of error. Modifications to the dimensionless terms to factor in propeller pitch were
presented, however more research was deemed necessary to apply this theory.
Corrigan and Altman (2008) examined different methods for wind tunnel blockage
corrections. These methods included the Glauert (1926) correction as well as a correction by
Hackett et al. (1979). These methods were described in detail and their applications were shown.
A wind tunnel experiment was designed and constructed to record the necessary variables to
calculate total propulsive efficiency. This is in contrast to other works that primarily explored
propeller efficiency. The stand was constructed using a beam-type load cell and a reaction torque
sensor. Three propellers (D = 10, 12, and 14 inches) were tested using different motors for each
propeller. Static pressure taps were used on the wall of the wind tunnel test section to record the
changes in pressure forward and aft of the propeller disk plane for the velocity corrections. The
Glauert method did not provide sufficient correction for large blockage conditions. The Hackett
method yielded more correction at higher airspeeds and larger propeller diameters, but the
method could not be validated and therefore further work was found to be necessary.
Merchant and Miller (2006) performed dynamic tests on propellers in the 6 ≤ D ≤ 22 inch
range. A test stand was constructed to record propeller performance parameters, where the thrust
and torque were collected by a combined thrust/torque cell. The load/torque cell was calibrated
using dead weights in the axial (thrust) and transverse (torque) directions. Wind tunnel velocity
was measured directly using a Pitot probe and a differential pressure transducer. Since the
propellers were large compared to the test section, blockage corrections developed by Glauert
(1926) were applied to the results. Readings were taken at wind-off-zero conditions before and
after each test. These values were then averaged and subtracted from the test data to account for
zero drift and temperature effects. Data was collected at constant propeller rotational speeds and
the wind tunnel velocity was varied to sweep through values of advance ratio. The results were
compared to other works and were shown to be acceptable. The setup was also tested for
variations in flow angularity. Pitch and yaw variations between −3 and +3 arc degrees were
6
examined and it was shown that only the coefficient of thrust was affected by a change in pitch.
However, it was shown that pitch variations of −3 and +3 degrees yielded the same results,
which indicated that the system was symmetric in the pitch direction. Lastly, two identical
propellers made by the same manufacturer were tested and compared, which showed that for
some propellers there may be significant differences in performance due to manufacturing. Very
limited results were presented, however, and the results shown only give a small sample of the
entire test range.
The objective of the present research was to determine the performance of various
commercially-available small-scale propellers driven by an electric motor. An experimental test
stand was designed and constructed in which the electric motor was mounted in a wind tunnel at
Wright State University for both static and dynamic testing. The freestream airspeed was varied
from zero to the windmill state for each propeller. The rotational speed was varied over the
operational range recommended by the propeller manufacturers, while ensuring that the electric
motor did not overheat. The primary measurement devices were calibrated, and an extensive
uncertainty analysis was performed. The results from the present experiment were compared to
those from previous studies for both static and dynamic data. For static testing, the coefficient of
thrust, the coefficient of propeller power and the total propulsive efficiency were plotted versus
the propeller rotational speed. For dynamic testing, the rotational speed of the propeller was held
constant at regular intervals while the freestream airspeed was increased from zero to the
maximum. The coefficient of thrust, the coefficient of propeller power and the propeller
efficiency were plotted versus the advance ratio for various rotational speeds.
BACKGROUND
The performance characteristics to be determined by the experimental setup are as
follows. The coefficients of thrust, torque and propeller power, and the propeller efficiency are
(Merchant and Miller, 2006):
The three performance coefficients and the propeller efficiency defined above are typically
plotted against the advance ratio for dynamic testing:
7
where the corrected freestream velocity is (Glauert, 1926):
[
(
)
√ ]
The uncorrected freestream velocity is:
√ i
The Glauert correction variable is:
The propeller disk area and wind tunnel area are, respectively:
The corrected thrust is defined as the measured thrust minus the drag force due to the flow of air
over the motor, torque cell and load cell (Selig and Ananda, 2011):
The total propulsive efficiency is the ratio of the propeller output power to the electrical input
power:
e
The density of air is given by the perfect gas law:
t t
EXPERIMENTAL SETUP
The objective of the present experiment was to determine the performance characteristics
of small electric motor/propeller combinations from static conditions to the windmill state. The
overall design of the dynamic test rig is shown in Figure 1. The electric motor was directly
attached to a 25 oz-in torque cell (Transducer Techniques, Model RTS-25), which was able to
withstand 10 kg in thrust and 1.7 kg in shear. The torque cell was in turn mounted onto a 1-kg
single point beam-type load cell (Transducer Techniques, Model LSP-1). Each cell was driven
8
by a signal conditioner (Transducer Techniques, Model TMO-1) that produced a 0 to 5 Volt
linear output. The assembly of the motor, torque cell and load cell is shown in Figure 2. The
motor was held in place with a custom-designed clam-shell clamp, in which fins were
incorporated to increase the convective heat transfer from the electric motor.
The load cell was attached to a section of 1.25-inch square aluminum tubing, which acted
as a riser to place the propeller in the middle of the test section. The bottom of the riser was
connected to an optical breadboard table (Melles-Griot, Model BBSS-25-610-1219) using
flanges of angle aluminum. A hole was milled in the acrylic floor of the wind tunnel for the
aluminum riser to pass through. The low-speed wind tunnel at Wright State University is an open
circuit design capable of producing speeds from 0.6 to 36 m/s with a contraction ratio of 6.25:1.
The square entrance of the wind tunnel has a 3.8 m2 opening with aluminum hexagonal
honeycomb sections that serve as a flow straightener. The height and width of the square test
section is W = 0.6096 m, and its length is 2.438 m. Doors on one side of the test section allow for
an entire wall to be opened for easy access.
The data acquisition system used to collect data from the instrumentation consisted of a
DAQ board (National Instruments, Model SCC-68) and a DAQ card (National Instruments,
Model PCI-6221) installed in a PC. Shielded wires were used to connect the outputs of the
transducers to the DAQ board. The electric motor driving the propeller was energized using a
precision DC power supply (Hewlett-Packard, Model 6012B). A servo tester (GWS, Model MT-
1) was used to control the rotational speed of the propeller (Corrigan and Altman, 2008). The
voltage supplied to the electric motor was measured using a digital multi-meter (National
Instruments, Model USB-4065). To measure the current, a DC Hall effect current transducer (CR
Magnetics, Model CR5210-30) with a range of 0 to 30 A was placed in-line between the power
supply and the motor speed controller.
A remote optical sensor (Monarch Instrument, Model ROS-W) connected to a panel
meter (Monarch Instrument, Model ACT-3X) was used to measure propeller rotational speed.
Reflective tape supplied with the sensor was placed near the hub on the leeward side of the
propeller so that the optical sensor did not have to be adjusted between runs.
Atmospheric pressure was measured to determine the density of the air. To record
atmospheric pressure, a barometer (Vaisala, Model PTB110) capable of measuring 500 to 1100
mbar with accuracy of ±0.3 mbar was used. The differential pressure produced by the Pitot tube
9
was measured using a differential pressure manometer (MKS, Model 226A). The height of the
Pitot tube from the floor of the wind tunnel was selected by traversing the boundary layer
thickness using the Pitot tube as outlined by Brezina (2012). The height was set to H = 2.5
inches, and the Pitot tube was made parallel to the wind tunnel walls by using a bubble level and
a custom-made jig.
The temperature of the motor was measured using a Type T thermocouple while the
temperature of the air inside the wind tunnel was measured using a Type E thermocouple probe
(Omega, Model EMQSS-125G-12). The Type T thermocouple junction was placed on the center
of the motor and was held in place by the aluminum clam-shell clamp. The Type E probe was
mounted in the floor of the wind tunnel ahead of the motor/propeller so that the sensing junction
extended into the airflow. The thermocouples were connected to thermocouple modules
(National Instruments, Model SCC-TC01) on the data acquisition board. The signals from the
eight sensors were read using custom-designed LabVIEW virtual instruments.
The twenty-four propellers selected for analysis ranged from 4.0 ≤ D ≤ 6.0 inches in
diameter and 2.0 ≤ P ≤ 5.5 inches in pitch, as shown in Table 1. Some of the propellers were
selected to overlap with previous research so that the procedures and test setup used for the
measurements could be compared and validated. The GWS 4.5 × 3.0 and GWS 5.0 × 4.3 inch
propellers were tested statically and compared to Deters and Selig (2008). An APC 8.0 × 3.8
inch Slow Flyer was tested dynamically and compared to the results posted on the UIUC
Propeller Database (Selig, 2012), while an APC 6.0 × 4.0 inch propeller was tested dynamically
and compared to the results presented by Ol et al. (2008).
UNCERTAINTY ANALYSIS
The uncertainties of all of the calculated results described in the above equations were
determined using the root-sum-square uncertainty method (Kline and McClintock, 1953). During
experimentation, eight primary measurements were made using the data acquisition system:
(c) Figure 11: The Effect of Varying Propeller Pitch while holding Diameter Constant (Dynamic
Testing): (a) Coefficient of Thrust, (b) Coefficient of Propeller Power, (c) Propeller Efficiency.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 0.2 0.4 0.6 0.8 1
Co
effi
cie
nt
of
Thru
st (
Dyn
amic
)
Advance Ratio
GWS 5.0 x 3.0 15998 RPMGWS 5.0 x 4.3 16006 RPMAPC 4.75 x 4.75 15997 RPMAPC 4.75 x 5.5 15990 RPM
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 0.2 0.4 0.6 0.8 1
Co
effi
cie
nt
of
Po
we
r (D
ynam
ic)
Advance Ratio
GWS 5.0 x 3.0 15998 RPMGWS 5.0 x 4.3 16006 RPMAPC 4.75 x 4.75 15997 RPMAPC 4.75 x 5.5 15990 RPM
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1
Pro
pe
ller
Effi
cie
ncy
Advance Ratio
GWS 5.0 x 3.0 15998 RPMGWS 5.0 x 4.3 16006 RPMAPC 4.75 x 4.75 15997 RPMAPC 4.75 x 5.5 15990 RPM
28
(a)
(b)
(c)
Figure 12: The Effect of Varying Propeller Diameter while holding Pitch Constant (Dynamic
Testing): (a) Coefficient of Thrust, (b) Coefficient of Propeller Power, (c) Propeller Efficiency.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.2 0.4 0.6 0.8 1 1.2
Co
effi
cie
nt
of
Thru
st (
Dyn
amic
)
Advance Ratio
APC 4.2 x 2.0 16023 RPMAPC 6.0 x 2.0 16009 RPMAPC 4.75 x 4.75 15997 RPMAPC 5.25 x 4.75 15988 RPMGWS 4.5 x 3.0 15996 RPMGWS 5.0 x 3.0 15998 RPM
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.2 0.4 0.6 0.8 1
Co
effi
cie
nt
of
Po
we
r (D
ynam
ic)
Advance Ratio
APC 4.2 x 2.0 16023 RPMAPC 6.0 x 2.0 16009 RPMAPC 4.75 x 4.75 15997 RPMAPC 5.25 x 4.75 15988 RPMGWS 4.5 x 3.0 15996 RPMGWS 5.0 x 3.0 15998 RPM
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1
Pro
pe
ller
Effi
cie
ncy
Advance Ratio
APC 4.2 x 2.0 16023 RPMAPC 6.0 x 2.0 16009 RPMAPC 4.75 x 4.75 15997 RPMAPC 5.25 x 4.75 15988 RPMGWS 4.5 x 3.0 15996 RPM
29
Figure 13: Coefficient of Thrust versus Advance Ratio for Square Propellers (D/P = 1.0) with
Propeller Di eter R nging ro 4.0 ≤ D ≤ 18 inches.
-0.1
-0.05
0
0.05
0.1
0.15
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Co
effi
cie
nt
of
Thru
st (
Dyn
amic
)
Advance Ratio
4.0x4.0 GWS WSU4.1x4.1 APC WSU4.7x4.7 Graupner WSU4.75x4.75 APC WSU4.75x4.75 CF APC WSU5.5x5.5 Graupner WSU8x8 APC Thin Electric Ol et al.8x8 APC Thin Electric UIUC8x8 APC Sport UIUC9x9 APC Thin Electric UIUC9x9 APC Sport UIUC10x10 APC Thin Electric Ol et al.10x10 APC Sport UIUC12x12 APC Thin Electric Ol et al.18x18 APC Ol et al.
30
(a)
(b)
(c)
Figure 14: Coefficient of Thrust versus Advance Ratio for the APC Sport 400 Electric Propellers
(ΔCT ≤ 20%): (a) Original Representation of CT; (b) CT Modified by D/P, (c) CT and J Modified
by D/P.
y = -0.035664x2 - 0.044141x + 0.121732R² = 0.528753
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.2 0.4 0.6 0.8 1 1.2
Co
effi
cie
nt
of
Thru
st
Advance Ratio
y = -0.062973x2 - 0.041761x + 0.136400R² = 0.679633
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.2 0.4 0.6 0.8 1 1.2
Co
effi
cie
nt
of
Thru
st *
(D/P
)
Advance Ratio
y = -0.123768x2 + 0.031706x + 0.124147R² = 0.720267
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.2 0.4 0.6 0.8 1 1.2
Co
effi
cie
nt
of
Thru
st *
(D/P
)
Advance Ratio * (D/P)
31
(a)
(b)
Figure 15: Coefficient of Propeller Power versus Advance Ratio for the APC Sport 400 Electric
ropellers (ΔCP ≤ 20%): (a) Original Representation of CP; (b) CP Modified by D/P.
y = 0.007516x2 - 0.029530x + 0.090244R² = 0.058844
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.2 0.4 0.6 0.8 1
Co
effi
cie
nt
of
Po
we
r
Advance Ratio
y = -0.058168x2 + 0.004500x + 0.105709R² = 0.537663
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.2 0.4 0.6 0.8 1
Co
effi
cie
nt
of
Po
we
r *
(D/P
)^2
Advance Ratio
32
(a)
(b)
Figure 16: Propeller Efficiency versus Advance Ratio for the APC Sport 400 Electric Propellers
(ΔηP ≤ 20%): (a) Original Representation of ηP; (b) Advance Ratio Modified by D/P.
y = -1.069536x2 + 1.757518x - 0.024676R² = 0.937662
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1 1.2
Pro
pe
ller
Effi
cie
ncy
Advance Ratio
y = -1.005349x2 + 1.723020x - 0.051306R² = 0.983048
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1 1.2
Pro
pe
ller
Effi
cie
ncy
Advance Ratio *(D/P)
33
Table 1: Summary of Propellers Studied.
Manufacturer Nominal D/P (in × in) Designation
APC 4.10 × 4.10 Speed 400 Electric
APC 4.20 × 2.00 Sport
APC 4.20 × 4.00 Free Flight
APC 4.50 × 4.10 Speed 400 Electric
APC 4.70 × 4.25 Speed 400 Electric
APC 4.75 × 4.75 Speed 400 Electric
APC 4.75 × 5.50 Speed 400 Electric
APC 5.10 × 4.50E Thin Electric
APC 5.25 × 4.75 Speed 400 Electric
APC 5.50 × 2.00 Free Flight
APC 5.50 × 4.50
Speed 400 Electric
APC 6.00 × 2.00
Sport
APC 6.00 × 4.00 E
Speed 400 Electric
APC 8.00 × 3.8
Slow Flyer
Graupner 4.00 × 3.00
Cam Speed
Graupner 4.70 × 4.00
Cam Speed
Graupner 4.70 × 4.70
Cam Speed
Graupner 5.50 × 4.30
Cam Speed
Graupner 5.50 × 5.50
Cam Speed
GWS 4.00 × 2.50
GWS 4.00 × 4.00
GWS 4.50 × 3.00
GWS 5.00 × 3.00
GWS 5.00 × 4.30
34
Table 2: Uncertainties of Primary Measurement Sensors and Calibration Sources.
Measurement Sensor Uncertainty
Thrust, T Transducer Techniques LSP 1kg Load Cell ΔTcal = ±7.70 g
Torque, Q Transducer Techniques RTS 25 oz-in
Reaction Torque Sensor ΔQcal = ±0.0498 g-m
Atmospheric Temperature, Tatm Omega Type E Thermocouple ΔTatm,cal = ±0.0334 °C
Calibration Mass Ohaus Digital Scale Δm = ±1.00 × 10-3
g
Propeller Diameter, D Digital Vernier Calipers ΔD = ±1.00 × 10-5
m
Propeller Rotational Speed, n Monarch Instruments Remote Optical Sensor
(ROS) and ACT 3x Panel Tachometer Δn = ± 1 RPM
Motor Voltage, V National Instruments USB-4065 Digital